The DS is the original replacement for the gameboy series, its quite clunky looking by todays standards.
This was replaced by the DS Lite which has a slimmer lighter body and improved screens.
The DSi is the latest incarnation. It has slightly larger screens than the Lite and has 2 low res cameras. It lost the formers backwards compatability but has gained a SD card slot for music playing.
Nintendo seem to be still selling both the Lite and i but if you want an original DS then it'll have to be secondhand.
The official site might help with which would suit you best.
http://www.nintendodsi.com/
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